I need some help with this question, look at the attached file for the diagram:
A beam of neutrons is moving with a speed of v = 3000 m/s and is diffracted from a crystal of table salt (NaCl), which has an interplanar spacing of d= 0.282 nm. (See figure.)
a. Find the de Broglie wavelength of the neutrons.
b. Find the angle of theta of the first interference maximum.
c. How many interference maxima can you observe? What is the largest diffraction angle for which an interference maximum can be observed?
This one first asks for the deBroglie wavelength. We know that deBroglie said, if light, which usually behaves as waves do, also hits in packets like particles, then maybe electrons, which seem to be in packets of charge "e", might also behave as waves do. Sure enough, beams of electrons interfere just like light waves do. Neutrons also do this. Thus every particle also has a wavelength, which is necessary to calculate interference effects such as in a diffraction experiment.
The deBroglie wavelength is given by lambda = h/p, where h is Planck's constant and p is the momentum of ...
This in-depth solution contains full explanations and calculations in showing the De Broglie Wavelength, angle of theta, and inference maxima for largest diffraction angle.